This three-volume edition contains edited versions of 128 papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany, from 31 August to 4 September 1987. The conference series is devoted to a review of the latest developments in the technique and theory of the boundary element methods (BEM) with emphasis on new advances and trends. This particular meeting was to be devoted to ''the engineering aspects versus mathematical formulations, in an effort to consolidate the basis of many new applications.'' Whether this goal was achieved is necessarily going to be determined by whether the reader has the mathematical ability to digest and interpret the several papers that address the mathematical bases of some of the newer applications. Each volume is divided into six to eight sections of related papers. One or two invited papers lead off most of the sections, followed by three to five contributed papers touching on both mathematical theory and applications of boundary elements. The references at the end of each contribution, when summed together, represent a substantial compilation of related literature representing a diversity of languages.